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Question
Find the simplest form of `(2sqrt(45)+3sqrt(20))/(2sqrt(5))`.
Solution
= `(2sqrt45 + 3sqrt20)/(2sqrt5)`
= `(2sqrt(9 xx 5) + 3sqrt(4 xx 5))/(2 sqrt 5)`
= `(2sqrt(3^2 xx 5) + 3sqrt(2^2 xx 5))/(2sqrt5)`
= `(2 xx 3sqrt5 + 3 xx 2sqrt5)/(2sqrt5)`
= `(2cancelsqrt5 (3 + 3))/(2cancelsqrt5)` = 6
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